Optimal Electrodynamic Tether Phasing and Orbit-Raising Maneuvers

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Abstract

We present optimal solutions for a point-mass electrodynamic tether (EDT) performing phasing and orbit-raising maneuvers. An EDT is a conductive tether on the order of 20 km in length and uses a Lorentz force to provide propellantless thrust. We develop the optimal equations of motion using Pontryagin's Minimum Principle. We find numerical solutions using a global, stochastic optimization method called Adaptive Simulated Annealing. The method uses Markov chains and the system's cost function to narrow down the search space. Newton's Method brings the error in the residual to below a specific tolerance. We compare the EDT solutions to similar constant-thrust solutions and investigate the patterns in the solution space. The EDT phasing maneuver has invariance properties similar to constant-thrust phasing maneuvers. Analyzing the solution space reveals that the EDT is faster at performing phasing maneuvers but slower at performing orbit-raising maneuvers than constant-thrust spacecraft. Also several bifurcation lines occur in the solution spaces for all maneuvers studied.